Recently, studies have been carried out that propose a causal and stable first order hydrodynamic theory [1]}, [2]}, [3]}, [4]}, [5]}. Motivated from these
studies, in this work, the stability and causality of the first order theory derived in previous section has been tested. At local rest frame for small wave number (\(k\) ) we have the frequency modes,
\(\omega ^{*{\parallel }{\perp }}_{1,2}=\frac{i}{2}\left[\frac{4\eta /3+\zeta }{(\epsilon _0+P_0)}\right]k^2\pm k c_s~,~\omega ^{*{\parallel }{\perp }}_3=i \left[\frac{\lambda T}{(\epsilon _0+P_0)}\right] k^2\) ,
which are always stable because of the positive imaginary parts of all the modes. At large \(k\) , the modes and the associated group velocity \(v_g\)  become,
\(\omega ^{*{\parallel }{\perp }}_{1,2}=\frac{i}{2}\bigg \lbrace \frac{B}{A}-\frac{E}{D}\bigg \rbrace \pm k\sqrt{\frac{D}{A}}~,~~~\omega ^{*{\parallel }{\perp }}_3=i\frac{E}{D}~,~~~v_g=\lim _{k\rightarrow \infty }\bigg \vert \frac{\partial \textrm {~Re}({\omega })}{\partial k}\bigg \vert =\sqrt{\frac{}{}}{D}{A}~.\) 
